Short Answer 
To find the equation of the line passing through points (0,4) and (1,6), first calculate the slope (m) as 2 using the formula m = (y2 – y1) / (x2 – x1). Then, determine the y-intercept (b) as 4, leading to the equation of the line: y = 2x + 4.
Step 1: Calculate the Slope
To determine the slope (m) of the line, use the slope formula: m = (y2 – y1) / (x2 – x1). Here, we can label the points as (x1, y1) = (0, 4) and (x2, y2) = (1, 6). Plugging in these values results in:
- m = (6 – 4) / (1 – 0)
- m = 2 / 1
- m = 2
Step 2: Find the Y-Intercept
Next, we need to determine the y-intercept (b) of the line using the slope-intercept form, y = mx + b. We’ll substitute one of the points, preferably the one where x = 0, which is (0, 4). By putting x and y values into the equation, we solve for b:
- 4 = 2(0) + b
- 4 = 0 + b
- b = 4
Step 3: Formulate the Equation
With the slope (m) and the y-intercept (b) calculated, you can now write the equation of the line. The equation takes the form y = mx + b, where you substitute the values you found:
- y = 2x + 4
This gives you the complete equation of the line that goes through the points (0, 4) and (1, 6).